I love Simcity and play it regularly, but that's a much narrower focus in scope. Simcity is about developing single cities and regions. Even in custom maps, the regions don't really get beyond 28x28 kilometers. Your computer would have a hard time handling any larger.
Civilization has a much larger global scope. You might not be able to detail individual cities, but you can spread across continents and seas in a way that SC4 can never allow. Simcity is for developing cities. Civilization is for developing empires.
Like the OP, I've sometimes played Civ4 with no other AI present. It's pretty relaxing and you can either focus on development to your hearts desire, or test out new strategies without the threat of Montezuma invading you at a moment's notice. Different people like different things.
I am surprised though that you can't play without the AI in Civ5. You can remove all the citystates, can't you? I would have thought they'd allow you to remove the other civs entirely as well